Parametric and non-parametric statistical tests are used to analyze data and test hypotheses. Parametric tests assume the data is normally distributed, while non-parametric tests do not. Common parametric tests include t-tests, ANOVA, and correlation tests. Common non-parametric tests include the Wilcoxon rank-sum test, Kruskal-Wallis test, chi-square test, Friedman test, and Spearman's rank correlation. Choosing the appropriate test depends on the research question, type of data, and whether the assumptions of parametric tests are met.

1. Statistical Test –
Divakar A K

2. Different Types of Statistical Tests: Concepts
Statistical tests are an important part of data analysis. They help us understand the data and make
inferences about the population. They are used to examine relationships between variables and test
hypotheses. They are a way of analyzing data to see if there is a significant difference between the
two groups. In statistics, there are two main types of tests: parametric and non-parametric. Both
types of tests are used to make inferences about a population based on a sample. The difference
between the two types of tests lies in the assumptions that they make about the data. Parametric
tests make certain assumptions about the data, while non-parametric tests do not make any
assumptions about the data. In this blog post, we will discuss the different types of statistical tests
and related concepts with the help of examples. As a data scientist, you must get a good
understanding of different types of statistical tests.

4. Parametric Vs Non- parametric
• Parametric Vs Non- parametric
• Normal distribution Vs skewed distribution
• Dependent and independent sample
• Repeated Measure Design

5. What are parametric statistical tests and what
are their different types?
• Parametric statistical tests are a group of statistical tests that make certain
assumptions about the data.
• These tests are used to make inferences about a population based on a
sample.
• The main assumption that these tests make is that the data is normally
distributed.
• This means that the data follows a specific pattern where the values are
evenly spread out around the mean.
• There are several different parametric statistical tests, including t-tests,
ANOVA, and Pearson’s correlation.

6. Independent t-tests:
• An independent t-test is a statistical test used to determine whether the means of two
groups are statistically different from each other.
• This test is often used when the data in each group are supplied by different people
or when the groups are randomly assigned.
• The benefits of using an independent t-test include that it is relatively easy to use and
has high statistical power
• For example, a researcher might be interested in comparing the average reading
scores of two groups of students – one group that is taking a course in English
literature and one group that is taking a course in math
• In this case, the researcher would use an independent t-test to compare the average
reading scores of the two groups
• The independent t-test allows for the comparison of two groups of unequal sizes
• The independent t-test is limited to the comparison of two groups and cannot be
used to compare more than two groups.

7. Paired t-tests:
• The paired t-test is a statistical test that is used to compare the means
of two groups
• The groups are usually matched or paired together in some way
• For example, you might have a group of people who receive a new
treatment and a group of people who receive a placebo treatment
• The two groups are then compared to see if there is a difference in the
mean scores
• The paired t-test is also used to compare the pre-treatment and post-
treatment scores of a single group of people.

8. ANOVA tests:
• compare the means of more than two groups
• There are several different types of ANOVA tests, including one-way ANOVA, two-way
ANOVA, and repeated measures ANOVA
• Each type of ANOVA test is used to compare different combinations of groups
• One real-world example of the one-way ANOVA in action is a study that can be conducted
to compare the GRE scores of students from different income levels and find whether
there are significant differences between the means of the three groups
• One possible outcome of the tests can be that the students from families with higher
incomes tended to score higher on the GRE than students from families with lower
incomes
• This study can be used to assess and examine inequalities in society.

9. MANOVA tests:
• Whether or not there are significant differences between two or more group
means
• It is similar to ANOVA, but it can be used with more than one dependent
variable
• MANOVA is a powerful statistical tool that can be used to examine the
relationships between multiple dependent variables and a single/multiple
independent variable
• MANOVA is an important statistical test that should be used when
investigating the relationships between multiple variables.

10. F-test:
• The F-test is used by a researcher in order to carry out the test for the
equality of the two population variances.
• If a researcher wants to test whether or not two independent samples have
been drawn from a normal population with the same variability, then he
generally employs the F-test.

11. Z-test:
• The Z-test is a statistical test that is used to determine the statistical
significance of a difference between two groups
• It is most commonly used when the groups are small
• This test is used to determine whether the difference between the
means of the two groups is statistically significant.

12. Correlation test (Pearson’s):
• Correlation tests are statistical tests that assess the strength of the relationship between
two variables
• The most common type of correlation test is Pearson’s Correlation Coefficient, which
measures the linear relationship between two variables
• Correlation tests are used in a variety of fields, including psychology, sociology, and
economics
• Correlation tests can be used to study the cause-and-effect relationship between two
variables or to predict future behavior based on past behavior
• For example, a correlation test could be used to determine if there is a relationship
between IQ and income
• Correlation tests are also used to predict future events
• For example, a correlation test could be used to predict the likelihood of a person getting
divorced based on their age and education level

13. Non-Parametric Statistical Tests
• Non-parametric tests do not make any assumptions about the data
• They can be used with data that is not normally distributed and with data that does not have equal
variances
• Non-parametric statistical tests are used when the assumptions of parametric statistical tests are not
met, or when the data are not normally distributed
• Some examples of non-parametric statistical tests include the Wilcoxon rank-sum test, the Kruskal-
Wallis test
• etc
• Statisticians have developed many different non-parametric statistical tests, each with its own
advantages and disadvantages
• When choosing a non-parametric statistical test, it is important to consider the specific research
question and the type of data that are available
• The following is a brief introduction to different types of non-parametric tests:

14. Wilcoxon rank-sum test:
• The Wilcoxon rank-sum test is a statistical test used to compare the
difference between two groups of data
• It is often used when the data is not normally distributed
• The test works by ranking the data from both groups, and then summing the
ranks for each group
• The difference between the two sums is then compared to a table of values to
determine whether or not there is a significant difference between the two
groups
• The Wilcoxon rank-sum test is a powerful statistical tool that can be used to
compare data sets of all sizes
• Wilcoxon rank-sum test is also known as the Mann-Whitney U test
(Independent sample).

15. Kruskal-Wallis test:
• The Kruskal-Wallis H test is a statistical test that can be used to compare the means of two or more
groups
• It is similar to the ANOVA, but it is more robust and can be used when the assumptions of the
ANOVA are not met
• The Kruskal-Wallis test is also known as a non-parametric ANOVA, or analysis of variance
• The Kruskal-Wallis test can be used with either continuous or categorical data
• To run the Kruskal-Wallis test, the data must be in the form of ranks
• The Kruskal-Wallis test is based on the ranks of the data, not the actual values
• When using categorical data, the Kruskal-Wallis test is often used to determine if there are
significant differences between the means of the groups
• When using quantitative data, the Kruskal-Wallis test can be used to determine if there are
significant differences between the distributions of the groups.

16. Chi-square test of independence:
• Chi-square test of independence is a statistical test used to determine whether two
variables are independent
• It is a non-parametric test, meaning that it does not make assumptions about the
distributions of the variables
• The chi-square test is used to calculate a statistic called the chi-square statistic
• This statistic is then compared to a critical value to determine whether the two
variables are independent
• If the chi-square statistic is greater than the critical value, then the two variables are
considered to be dependent
• Chi-square test of independence can be used to test for independence in a variety of
situations, including comparing proportions, testing for association, and testing for
goodness of fit.

17. The Friedman Test
• : The Friedman test is a non-parametric statistical test used to
compare more than two groups of data
• The test is used when the data are not normally distributed and when
the groups are related to each other, such as in a repeated measures
design
• The test is based on the ranks of the data, rather than the actual values

18. Spearmans row
• Spearman rank correlation is a non-parametric test that is used to
measure the degree of association between two variables

20. source
• https://vitalflux.com/different-types-of-statistical-tests-concepts-
examples/
• https://www.statisticssolutions.com/free-resources/directory-of-
statistical-analyses/kruskal-wallis-test/
• https://www.indeed.com/career-advice/career-
development/confidence-level-versus-confidence-interval
• https://www.scribbr.com/statistics/p-value/
• https://www.youtube.com/watch?v=L2pbK4ARzI8
• https://statistics.laerd.com/spss-tutorials/testing-for-normality-using-
spss-statistics-2.php